In `(5)/(7)xy^(2)z^(3)`, write the coefficient of :
`(1)/(7)yz`

Answer

To find the coefficient of \(\frac{1}{7}yz\) in the expression \(\frac{5}{7}xy^2z^3\), we can follow these steps:

### Step 1: Identify the given expression
The given expression is:
\[ \frac{5}{7}xy^2z^3 \]

### Step 2: Rewrite the expression in terms of the required term
We need to find the coefficient of the term \(\frac{1}{7}yz\). Notice that:
- \(y^2\) can be rewritten as \(y \cdot y\)
- \(z^3\) can be rewritten as \(z \cdot z \cdot z\)

So we can express \(\frac{5}{7}xy^2z^3\) as:
\[ \frac{5}{7} \cdot x \cdot y \cdot y \cdot z \cdot z \cdot z \]

### Step 3: Isolate the term \(\frac{1}{7}yz\)
To isolate \(\frac{1}{7}yz\), we can factor out \(\frac{1}{7}yz\) from the expression:
\[ \frac{5}{7}xy^2z^3 = \frac{1}{7}yz \cdot (5x \cdot y \cdot z^2) \]

### Step 4: Identify the coefficient
From the above expression, the coefficient of \(\frac{1}{7}yz\) is:
\[ 5xy \cdot z^2 \]

### Step 5: Simplify the coefficient
Since we are looking for the coefficient of \(\frac{1}{7}yz\), we can see that the remaining terms after factoring out \(\frac{1}{7}yz\) are:
\[ 5x \cdot z^2 \]

Thus, the coefficient of \(\frac{1}{7}yz\) in the expression \(\frac{5}{7}xy^2z^3\) is:
\[ 5xz^2 \]

### Final Answer
The coefficient of \(\frac{1}{7}yz\) in \(\frac{5}{7}xy^2z^3\) is \(5xz^2\).

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